Special Issue 2022 – Call for Papers
A New Role for Statistics: The Joint Special Issue of "Statistics in Transition New Series" (SiTns) and "Statystyka Ukraïny" (SU)
Yeil Kwon https://orcid.org/0000-0002-1663-5401

© Kwon Yeil. Article available under the CC BY-SA 4.0 licence

ARTICLE

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ABSTRACT

A Fibonacci-type probability distribution provides the probabilistic models for establishing stopping rules associated with the number of consecutive successes. It can be interpreted as a generalized version of a geometric distribution. In this article, after revisiting the Fibonaccitype probability distribution to explore its definition, moments and properties, we proposed numerical methods to obtain two estimators of the success probability: the method of moments estimator (MME) and maximum likelihood estimator (MLE). The ways both of them performed were compared in terms of the mean squared error. A numerical study demonsrated that the MLE tends to outperform the MME for most of the parameter space with various sample sizes.

KEYWORDS

Fibonacci probability distribution, generalized polynacci distribution, factorial moment generating function, method of moments, maximum likelihood estimator

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